In a bumper test, three types of autos were deliberately crashed into a barrier
ID: 2929028 • Letter: I
Question
In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research question: Are the mean crash damages the same for these three vehicles?
Please clearly answer all questions in order, thank you very much.
In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research question: Are the mean crash damages the same for these three vehicles?
Explanation / Answer
Step 1
Null Hypothesis Ho :µ1 =µ2 =µ3
Alternative Hypothesis :µ1 µ2 µ3
Step 2
Degrees of freedom between = k - 1 = 3 - 1 = 2
Degrees of freedom Within = n - k = 15 - 3 = 12
Degrees of freedom Total F( k-1,n - k,) at 0.05 is = F Crit = 3.885
Step 3
Grand Mean = G / N = 1308+1392+1646 / 3 = 1448.667
SST = ( Xi - GrandMean)^2 = (1660-1448.667)^2 + (770-1448.667)^2 + (880-1448.667)^2 + ……..& so on = 2645373.333
SS Within = (Xi - Mean of Xi ) ^2 =,(1660-1308)^2 + (770-1308)^2 + (880-1308)^2 + ……..& so on = 2335680
SS Between = SST - SS Within = 2645373.333 - 2335680 = 309693.333
Step 4
Mean Square Between = SS Between / df Between = 309693.333/2 = 154846.667
Mean Square Within = SS Within / df Within = 2335680/12 = 194640
Step 5
F Cal = MS Between / Ms Within = 154846.667/194640 = 0.796
We got |F cal| = 0.796 & |F Crit| =3.885
MAKE DECISION
Hence Value of |F cal| < |F Crit|and Here We Accept Ho
Treatments ONE WAY ANOVA Mean = X /n Goliath 1660 770 880 1980 1250 1308 Varmint 1270 1480 1380 1850 980 1392 Weasel 1020 2140 1880 1290 1900 1646